lecture 18 - pushdown automata - examples

Pushdown Automata - ExamplesLecture 18Section 2.2

Robb T. Koether

Hampden-Sydney College

Mon, Oct 8, 2012

Robb T. Koether (Hampden-Sydney College) Pushdown Automata - Examples Mon, Oct 8, 2012 1 / 14

Outline

1 Examples of PDAsEqual Number of a’s and b’sBalanced ParenthesesAlgebraic Expressions

2 Assignment


Outline


2 Assignment


Examples

Example (Pushdown automaton)Design a PDA that accepts the language

{w | w contains an equal number of a’s and b’s}.


Examples

Example (Pushdown automaton)The strategy will be to keep the excess symbols, either a’s or b’s,on the stack.One state will represent an excess of a’s.Another state will represent an excess of b’s.We can tell when the excess switches from one symbol to theother because at that point the stack will be empty.In fact, when the stack is empty, we may return to the start state.


Examples

Example (Pushdown automaton)

b, $ → εa, ε → $

b, ε → $

a, ε → ab, a → ε

b, ε → ba, b → ε

a < b

a > b

a, $ → ε


Examples

Example (Pushdown automaton)Note that this solution is inspired by the grammar

S → SS | aSb | bSa | ε


Outline


2 Assignment


Examples

Example (Pushdown automata)Let Σ = {a, (, )}. Design a PDA whose language is

{w | w contains balanced parentheses}.


Outline


2 Assignment


Examples

Example (Pushdown automata)Let Σ = {a, b, c, +,×, (, )}. Design a PDA whose language is

{w | w is a valid algebraic expression}.


Outline


2 Assignment


Assignment

AssignmentRead Section 2.2, pages 112 - 114.Problems 21, 22, 23, 24, page 130.Let Σ = {a, (, ), [, ]}. Design a PDA whose language is

{w | w contains balanced parentheses and brackets}.

Design a PDA whose language is

{anbmcmdn | m, n ≥ 0}.

Design a PDA whose language is

{anbm | n 6= m}.


lecture 18 - pushdown automata - examples

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pdas equal number

sydney college

pushdown automaton

pushdown automata

excess

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